Sz\303\241m\303\255t\303\263g\303\251pes sz\303\241melm\303\251let J\303\241rai Antal Ezek a programok csak szeml\303\251ltet\303\251sre szolg\303\241lnak
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">1. A pr\303\255mek eloszl\303\241sa, szit\303\241l\303\241s</Font></Text-field>
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">2. Egyszer\305\261 faktoriz\303\241l\303\241si m\303\263dszerek</Font></Text-field>
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">3. Egyszer\305\261 pr\303\255mtesztel\303\251si m\303\263dszerek</Font></Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 1" layout="Heading 1">4. Lucas-sorozatok</Text-field>
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">5. Alkalmaz\303\241sok </Font></Text-field>
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">6. Sz\303\241mok \303\251s polinomok</Font></Text-field>
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">7. Gyors Fourier-transzform\303\241ci\303\263</Font></Text-field>
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">8. Elliptikus f\303\274ggv\303\251nyek</Font></Text-field>
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">9. Sz\303\241mol\303\241s elliptikus g\303\266rb\303\251ken</Font></Text-field>
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">10. Faktoriz\303\241l\303\241s elliptikus g\303\274rb\303\251kkel</Font></Text-field>
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">11. Pr\303\255mteszt elliptikus g\303\266rb\303\251kkel</Font></Text-field>
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">12. Polinomfaktoriz\303\241l\303\241s</Font></Text-field> restart; with(PolynomialTools); NzNJMENvZWZmaWNpZW50TGlzdEc2IkkyQ29lZmZpY2llbnRWZWN0b3JHRiRJLUdjZEZyZWVCYXNpc0dGJEk/R3JlYXRlc3RGYWN0b3JpYWxGYWN0b3JpemF0aW9uR0YkSShIdXJ3aXR6R0YkSTFJc1NlbGZSZWNpcHJvY2FsR0YkSTJNaW5pbWFsUG9seW5vbWlhbEdGJEkwUERFVG9Qb2x5bm9taWFsR0YkSTBQb2x5bm9taWFsVG9QREVHRiRJMFNoaWZ0RXF1aXZhbGVudEdGJEk3U2hpZnRsZXNzRGVjb21wb3NpdGlvbkdGJEkoU2hvcnRlbkdGJEkoU2hvcnRlckdGJEklU29ydEdGJEkmU3BsaXRHRiRJJ1NwbGl0c0dGJEkqVHJhbnNsYXRlR0Yk
<Text-field style="Heading 2" layout="Heading 2">12.1. <Font encoding="UTF-8">Polinomfaktoriz\303\241l\303\241s modulo egy pr\303\255m.</Font></Text-field>
<Text-field style="Heading 2" layout="Heading 2">12.2. Visszavezet<Font encoding="UTF-8">\303\251</Font>s n<Font encoding="UTF-8">\303\251</Font>gyzetmentes esetre.</Text-field> SquareFree:=proc(a,x,p) local i,out,b,c,y,z,w; i:=1; out:=[]; b:=diff(a,x) mod p; if b=0 then error "zero derivative; substitute x^p with p"; fi; c:=Gcd(a,b) mod p; w:=Quo(a,c,x) mod p; while degree(c)<>0 do y:=Gcd(w,c) mod p; z:=Quo(w,y,x) mod p; out:=[op(out),z]; i:=i+1; w:=y; c:=Quo(c,y,x) mod p; od; out:=[c,op(out),w]; end; 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 `mod`:=mods; x:='x'; a:=x^15-1; debug(SquareFree); SquareFree(a,x,5); SSVtb2RzRyUqcHJvdGVjdGVkRw== SSJ4RzYi LCYqJClJInhHNiIiIzoiIiJGKEYoISIi SStTcXVhcmVGcmVlRzYi {--> enter SquareFree, args = x^15-1, x, 5 IiIi NyI= IiIh <-- ERROR in SquareFree (now at top level) = zero derivative; substitute x^p with p} Error, (in SquareFree) zero derivative; substitute x^p with p SquareFree(a,x,11); {--> enter SquareFree, args = x^15-1, x, 11 IiIi NyI= LCQqJiIiJSIiIilJInhHNiIiIzlGJUYl IiIi LCYqJClJInhHNiIiIzoiIiJGKEYoISIi NyQiIiIsJiokKUkieEc2IiIjOkYjRiNGIyEiIg== <-- exit SquareFree (now at top level) = [1, x^15-1]} NyQiIiIsJiokKUkieEc2IiIjOkYjRiNGIyEiIg== SquareFree(x^3+3*x^2+3*x+1,x,11); {--> enter SquareFree, args = x^3+3*x^2+3*x+1, x, 11 IiIi NyI= LCgqJiIiJCIiIilJInhHNiIiIiNGJUYlKiYiIiZGJUYnRiUhIiJGJEYl LCgqJClJInhHNiIiIiMiIiJGKComRidGKEYlRihGKEYoRig= LCZJInhHNiIiIiJGJUYl LCZJInhHNiIiIiJGJUYl IiIi NyMiIiI= IiIj LCZJInhHNiIiIiJGJUYl LCZJInhHNiIiIiJGJUYl LCZJInhHNiIiIiJGJUYl IiIi NyQiIiJGIw== IiIk LCZJInhHNiIiIiJGJUYl IiIi NyYiIiJGI0YjLCZJInhHNiJGI0YjRiM= <-- exit SquareFree (now at top level) = [1, 1, 1, x+1]} NyYiIiJGI0YjLCZJInhHNiJGI0YjRiM=
<Text-field style="Heading 2" layout="Heading 2">12.3. V<Font encoding="UTF-8">\303\251</Font>ges testek.</Text-field> n:=8; RijndaelPoly:=Nextprime(Z^n,Z) mod 2; alpha:=Z; IiIp LCwqJClJIlpHNiIiIikiIiJGKCokKUYlIiIlRihGKCokKUYlIiIkRihGKEYlRihGKEYo SSJaRzYi x:=234; xx:=convert(x,base,2); xxx:=add(xx[i]*Z^(i-1),i=1..nops(xx)); IiRNIw== NyoiIiEiIiJGI0YkRiNGJEYkRiQ= LCxJIlpHNiIiIiIqJClGIyIiJEYlRiUqJClGIyIiJkYlRiUqJClGIyIiJ0YlRiUqJClGIyIiKEYlRiU= y:=111; yy:=convert(y,base,2); yyy:=add(yy[i]*Z^(i-1),i=1..nops(yy)); IiQ2Ig== NykiIiJGI0YjRiMiIiFGI0Yj LC4iIiJGI0kiWkc2IkYjKiQpRiQiIiNGI0YjKiQpRiQiIiRGI0YjKiQpRiQiIiZGI0YjKiQpRiQiIidGI0Yj zzz:=modpol(xxx+yyy,RijndaelPoly,Z,2); zz:=CoefficientList(zzz,Z); z:=add(zz[i]*2^(i-1),i=1..nops(zz)); LCgqJClJIlpHNiIiIigiIiJGKEYoRigqJClGJSIiI0YoRig= NyoiIiIiIiFGI0YkRiRGJEYkRiM= IiRMIg== zzz:=modpol(xxx*yyy,RijndaelPoly,Z,2); zz:=CoefficientList(zzz,Z); z:=add(zz[i]*2^(i-1),i=1..nops(zz)); LC4qJClJIlpHNiIiIiciIiJGKCokKUYlIiImRihGKCokKUYlIiIlRihGKCokKUYlIiIkRihGKCokKUYlIiIjRihGKEYoRig= NykiIiIiIiFGI0YjRiNGI0Yj IiREIg== zzz:=modpol(1/xxx,RijndaelPoly,Z,2); zz:=CoefficientList(zzz,Z); z:=add(zz[i]*2^(i-1),i=1..nops(zz)); LC4qJClJIlpHNiIiIigiIiJGKCokKUYlIiInRihGKCokKUYlIiIlRihGKCokKUYlIiIjRihGKEYlRihGKEYo NyoiIiJGI0YjIiIhRiNGJEYjRiM= IiQ6Iw==
<Text-field style="Heading 2" layout="Heading 2">12.4. Fak<Font encoding="UTF-8">toriz\303\241l\303\241s k\303\274</Font>l<Font encoding="UTF-8">\303\266</Font>nb<Font encoding="UTF-8">\303\266</Font>z<Font encoding="UTF-8">\305\221</Font> fok<Font encoding="UTF-8">\303\272</Font> faktorokra.</Text-field> PartialFactorDD:=proc(a,x,p) local aa,L,aaa,w,i; i:=1; w:=x; aa:=a; L:=[]; while i<=degree(aa)/2 do w:=Rem(w^p,aa,x) mod p; aaa:=Gcd(aa,w-x) mod p; L:=[op(L),aaa]; if aaa<>1 then aa:=Quo(aa,aaa,x) mod p: w:=Rem(w,aa,x) mod p; fi; i:=i+1; od; L:=[op(L),aa]; end; Zio2JUkiYUc2IkkieEdGJUkicEdGJTYnSSNhYUdGJUkiTEdGJUkkYWFhR0YlSSJ3R0YlSSJpR0YlRiVGJUMoPkYtIiIiPkYsRiY+RilGJD5GKjciPyhGJUYwRjBGJTFGLSwkKiYjRjAiIiNGMC1JJ2RlZ3JlZUclKnByb3RlY3RlZEc2I0YpRjBGMEMnPkYsLUkkbW9kR0YlNiQtSSRSZW1HNiRGPUkoX3N5c2xpYkdGJTYlKUYsRidGKUYmRic+RistRkI2JC1JJEdjZEdGRjYkRiksJkYsRjBGJiEiIkYnPkYqNyQtSSNvcEdGPTYjRipGK0AkMEYrRjBDJD5GKS1GQjYkLUkkUXVvR0ZGNiVGKUYrRiZGJz5GLC1GQjYkLUZFNiVGLEYpRiZGJz5GLSwmRi1GMEYwRjA+Rio3JEZURilGJUYlRiU= `mod`:=mods; x:='x'; a:=x^15-1; debug(PartialFactorDD); PartialFactorDD(a,x,11); SSVtb2RzRyUqcHJvdGVjdGVkRw== SSJ4RzYi LCYqJClJInhHNiIiIzoiIiJGKEYoISIi STBQYXJ0aWFsRmFjdG9yRERHNiI= {--> enter PartialFactorDD, args = x^15-1, x, 11 IiIi SSJ4RzYi LCYqJClJInhHNiIiIzoiIiJGKEYoISIi NyI= KiQpSSJ4RzYiIiM2IiIi LCYqJClJInhHNiIiIiYiIiJGKEYoISIi NyMsJiokKUkieEc2IiIiJiIiIkYpRikhIiI= LCgqJClJInhHNiIiIzUiIiJGKCokKUYlIiImRihGKEYoRig= LCYqJClJInhHNiIiIiciIiIhIiJGJUYp IiIj SSJ4RzYi LCgqJClJInhHNiIiIzUiIiJGKCokKUYlIiImRihGKEYoRig= NyQsJiokKUkieEc2IiIiJiIiIkYpRikhIiIsKCokKUYmIiM1RilGKUYkRilGKUYp IiIi IiIh IiIk NyUsJiokKUkieEc2IiIiJiIiIkYpRikhIiIsKCokKUYmIiM1RilGKUYkRilGKUYpRik= <-- exit PartialFactorDD (now at top level) = [x^5-1, x^10+x^5+1, 1]} NyUsJiokKUkieEc2IiIiJiIiIkYpRikhIiIsKCokKUYmIiM1RilGKUYkRilGKUYpRik=
<Text-field style="Heading 2" layout="Heading 2">12.5. Has<Font encoding="UTF-8">\303\255</Font>t<Font encoding="UTF-8">\303\241</Font>s.</Text-field> PartialFactorSplit:=proc(a,x,d,p) local t,i; t:=rand(); t:=convert(t,base,p); t:=add(t[i]*x^(i-1),i=1..nops(t)); t:=modpol(t,a,x,p); t:=modpol(t^((p^d-1)/2)-1,a,x,p); t:=Gcd(t,a) mod p; [t,Quo(a,t,x) mod p]; end; Zio2JkkiYUc2IkkieEdGJUkiZEdGJUkicEdGJTYkSSJ0R0YlSSJpR0YlRiVGJUMpPkYqLUklcmFuZEdGJUYlPkYqLUkoY29udmVydEclKnByb3RlY3RlZEc2JUYqSSViYXNlR0YlRig+RiotSSRhZGRHRjM2JComJkYqNiNGKyIiIilGJiwmRitGPUY9ISIiRj0vRis7Rj0tSSVub3BzR0YzNiNGKj5GKi1JJ21vZHBvbEc2JEYzSShfc3lzbGliR0YlNiZGKkYkRiZGKD5GKi1GSDYmLCYpRiosJiomI0Y9IiIjRj0pRihGJ0Y9Rj1GU0ZARj1GPUZARiRGJkYoPkYqLUkkbW9kR0YlNiQtSSRHY2RHRkk2JEYqRiRGKDckRiotRlg2JC1JJFF1b0dGSTYlRiRGKkYmRihGJUYlRiU= debug(PartialFactorSplit); PartialFactorSplit(x^5-1,x,1,11); STNQYXJ0aWFsRmFjdG9yU3BsaXRHNiI= {--> enter PartialFactorSplit, args = x^5-1, x, 1, 11 Ii1NMCcpPWRS Ny4iIikiIiEiIzUiIidGI0YlRiZGJCIiKiIiIyIiJSIiIg== LDYiIikiIiIqJiIjNUYkKUkieEc2IiIiI0YkRiQqJiIiJ0YkKUYoIiIkRiRGJComRiNGJClGKCIiJUYkRiQqJkYmRiQpRigiIiZGJEYkKiZGLEYkKUYoRixGJEYkKiYiIipGJClGKEYjRiRGJComRipGJClGKEY4RiRGJComRjFGJClGKEYmRiRGJCokKUYoIiM2RiRGJA== LCoqJClJInhHNiIiIiMiIiIhIiIqJiIiJUYoKUYlIiIkRihGKCokKUYlRitGKEYpKiZGK0YoRiVGKEYp LCwqJiIiJiIiIilJInhHNiIiIiVGJSEiIiokKUYnIiIkRiVGJSomIiIjRiUpRidGL0YlRioqJkYpRiVGJ0YlRipGJUYq LCgqJClJInhHNiIiIiMiIiJGKComIiImRihGJUYoISIiIiIlRig= NyQsKCokKUkieEc2IiIiIyIiIkYpKiYiIiZGKUYmRikhIiIiIiVGKSwqKiQpRiYiIiRGKUYpKiZGK0YpRiVGKUYpRiZGLEYxRiw= <-- exit PartialFactorSplit (now at top level) = [x^2-5*x+4, x^3+5*x^2-x-3]} NyQsKCokKUkieEc2IiIiIyIiIkYpKiYiIiZGKUYmRikhIiIiIiVGKSwqKiQpRiYiIiRGKUYpKiZGK0YpRiVGKUYpRiZGLEYxRiw= expand((x^2+2*x-2)*(x^3-2*x^2-5*x-5)) mod 11; LCYqJClJInhHNiIiIiYiIiJGKEYoISIi PartialFactorSplit(x^2+2*x-2,x,1,11); PartialFactorSplit(x^3-2*x^2-5*x-5,x,1,11); {--> enter PartialFactorSplit, args = x^2+2*x-2, x, 1, 11 Ii06ayIpUko+ Ny0iIigiIipGIyIiJEYlIiIlIiIiIiIhIiM1RiZGIw== LDYiIigiIiIqJiIiKkYkSSJ4RzYiRiRGJComRiNGJClGJyIiI0YkRiQqJiIiJEYkKUYnRi1GJEYkKiZGLUYkKUYnIiIlRiRGJComRjFGJClGJyIiJkYkRiQqJClGJyIiJ0YkRiQqJiIjNUYkKUYnIiIpRiRGJComRjFGJClGJ0YmRiRGJComRiNGJClGJ0Y5RiRGJA== LCYiIiMhIiIqJiIiJiIiIkkieEc2IkYnRiQ= LCZJInhHNiIhIiIiIiQiIiI= IiIi NyQiIiIsKCokKUkieEc2IiIiI0YjRiMqJkYpRiNGJ0YjRiNGKSEiIg== <-- exit PartialFactorSplit (now at top level) = [1, x^2+2*x-2]} NyQiIiIsKCokKUkieEc2IiIiI0YjRiMqJkYpRiNGJ0YjRiNGKSEiIg== {--> enter PartialFactorSplit, args = x^3-2*x^2-5*x-5, x, 1, 11 IixsLzxDQyM= NywiIiUiIioiIiIiIiEiIiZGJCIiKCIiJ0YnRiQ= LDQiIiUiIiIqJiIiKkYkSSJ4RzYiRiRGJCokKUYnIiIjRiRGJComIiImRiQpRidGI0YkRiQqJkYmRiQpRidGLUYkRiQqJiIiKEYkKUYnIiInRiRGJComRjRGJClGJ0YyRiRGJComRi1GJClGJyIiKUYkRiQqJkYmRiQpRidGJkYkRiQ= LCYqJiIiIyIiIkkieEc2IkYlISIiRiRGJQ== LCgqJiIiIyIiIilJInhHNiJGJEYlISIiKiZGJEYlRidGJUYlRiVGKQ== IiIi NyQiIiIsKiokKUkieEc2IiIiJEYjRiMqJiIiI0YjKUYnRitGIyEiIiomIiImRiNGJ0YjRi1GL0Yt <-- exit PartialFactorSplit (now at top level) = [1, x^3-2*x^2-5*x-5]} NyQiIiIsKiokKUkieEc2IiIiJEYjRiMqJiIiI0YjKUYnRitGIyEiIiomIiImRiNGJ0YjRi1GL0Yt expand((x-4)*(x-5)) mod 11; expand((x+2)*(x^2-4*x+3)) mod 11; LCgqJClJInhHNiIiIiMiIiJGKComRidGKEYlRihGKEYnISIi LCoqJClJInhHNiIiIiQiIiJGKComIiIjRigpRiVGKkYoISIiKiYiIiZGKEYlRihGLEYuRiw= PartialFactorSplit(x^2-4*x+3,x,1,11); {--> enter PartialFactorSplit, args = x^2-4*x+3, x, 1, 11 Ii1mV1soPSsp Ny4iIiEiIiQiIiciIioiIigiIzUiIiNGKEYkRiYiIilGKQ== LDgqJiIiJCIiIkkieEc2IkYlRiUqJiIiJ0YlKUYmIiIjRiVGJSomIiIqRiUpRiZGJEYlRiUqJiIiKEYlKUYmIiIlRiVGJSomIiM1RiUpRiYiIiZGJUYlKiZGK0YlKUYmRilGJUYlKiZGNEYlKUYmRjBGJUYlKiZGJEYlKUYmIiIpRiVGJSomRi1GJSlGJkYtRiVGJSomRj1GJSlGJkY0RiVGJSomRitGJSlGJiIjNkYlRiU= LCYqJiIiIyIiIkkieEc2IkYlISIiIiImRiU= LCZJInhHNiIhIiIiIiJGJg== LCZJInhHNiIiIiJGJSEiIg== NyQsJkkieEc2IiIiIkYmISIiLCZGJEYmIiIkRic= <-- exit PartialFactorSplit (now at top level) = [x-1, x-3]} NyQsJkkieEc2IiIiIkYmISIiLCZGJEYmIiIkRic= PartialFactorSplit(x^2-4*x+3,x,1,11); {--> enter PartialFactorSplit, args = x^2-4*x+3, x, 1, 11 Ii1wbzBfdlU= Ny4iIiRGIyIiJiIiKSIiKiIjNSIiIiIiJ0YjRiRGJEYo LDoiIiQiIiIqJkYjRiRJInhHNiJGJEYkKiYiIiZGJClGJiIiI0YkRiQqJiIiKUYkKUYmRiNGJEYkKiYiIipGJClGJiIiJUYkRiQqJiIjNUYkKUYmRilGJEYkKiQpRiYiIidGJEYkKiZGOEYkKUYmIiIoRiRGJComRiNGJClGJkYtRiRGJComRilGJClGJkYwRiRGJComRilGJClGJkY0RiRGJCokKUYmIiM2RiRGJA== LCQqJiIiJSIiIkkieEc2IkYlRiU= IiIh LCgqJClJInhHNiIiIiMiIiJGKComIiIlRihGJUYoISIiIiIkRig= NyQsKCokKUkieEc2IiIiIyIiIkYpKiYiIiVGKUYmRikhIiIiIiRGKUYp <-- exit PartialFactorSplit (now at top level) = [x^2-4*x+3, 1]} NyQsKCokKUkieEc2IiIiIyIiIkYpKiYiIiVGKUYmRikhIiIiIiRGKUYp expand((x-3)*(x-1)) mod 11; LCgqJClJInhHNiIiIiMiIiJGKComIiIlRihGJUYoISIiIiIkRig= PartialFactorSplit(x^10+x^5+1,x,2,11); {--> enter PartialFactorSplit, args = x^10+x^5+1, x, 2, 11 Ii1VV29BRSUp Ny4iIiEiIiVGJCIiIiIjNSIiJiIiKkYoIiIkRidGJiIiIw== LDgqJiIiJSIiIkkieEc2IkYlRiUqJkYkRiUpRiYiIiNGJUYlKiQpRiYiIiRGJUYlKiYiIzVGJSlGJkYkRiVGJSomIiImRiUpRiZGMkYlRiUqJiIiKkYlKUYmIiInRiVGJSomRjVGJSlGJiIiKEYlRiUqJkYtRiUpRiYiIilGJUYlKiZGMkYlKUYmRjVGJUYlKiZGL0YlKUYmRi9GJUYlKiZGKkYlKUYmIiM2RiVGJQ== LDYqJiIiJiIiIilJInhHNiIiIipGJUYlKiYiIiRGJSlGJyIiKUYlRiUqJiIiI0YlKUYnIiIoRiUhIiIqJiIiJUYlKUYnIiInRiVGMiomRiRGJSlGJ0YkRiVGMiokKUYnRjRGJUYyKiQpRidGK0YlRiUqJkY0RiUpRidGL0YlRiUqJkYvRiVGJ0YlRiVGJUYl LC4qJiIiJCIiIilJInhHNiIiIipGJSEiIiomRiRGJSlGJyIiKEYlRioqJiIiJUYlKUYnIiInRiVGKiokKUYnRiRGJUYlKiZGJEYlKUYnIiIjRiVGKkYlRiU= LCwqJClJInhHNiIiIiUiIiJGKComIiIjRigpRiUiIiRGKCEiIiomIiImRigpRiVGKkYoRi0qJkYnRihGJUYoRihGJ0Yo NyQsLCokKUkieEc2IiIiJSIiIkYpKiYiIiNGKSlGJiIiJEYpISIiKiYiIiZGKSlGJkYrRilGLiomRihGKUYmRilGKUYoRiksMCokKUYmIiInRilGKSomRitGKSlGJkYwRilGKSomRitGKUYlRilGLkYqRikqJkYoRilGMUYpRikqJkYtRilGJkYpRi5GLUYp <-- exit PartialFactorSplit (now at top level) = [x^4-2*x^3-5*x^2+4*x+4, x^6+2*x^5-2*x^4+2*x^3+4*x^2-3*x+3]} NyQsLCokKUkieEc2IiIiJSIiIkYpKiYiIiNGKSlGJiIiJEYpISIiKiYiIiZGKSlGJkYrRilGLiomRihGKUYmRilGKUYoRiksMCokKUYmIiInRilGKSomRitGKSlGJkYwRilGKSomRitGKUYlRilGLkYqRikqJkYoRilGMUYpRikqJkYtRilGJkYpRi5GLUYp expand((x^6-2*x^5+3*x^4+x^3-2*x^2+4*x+5)*(x^4+2*x^3+x^2-5*x-2)) mod 11; LCgqJClJInhHNiIiIzUiIiJGKCokKUYlIiImRihGKEYoRig= PartialFactorSplit(x^6-2*x^5+3*x^4+x^3-2*x^2+4*x+5,x,2,11); PartialFactorSplit(x^4+2*x^3+x^2-5*x-2,x,2,11); {--> enter PartialFactorSplit, args = x^6-2*x^5+3*x^4+x^3-2*x^2+4*x+5, x, 2, 11 Ii1TZUcnRzcl Ny4iIiEiIiUiIilGIyIiJiIiKkYlIiIkRidGJ0YkIiIi LDYqJiIiJSIiIkkieEc2IkYlRiUqJiIiKUYlKUYmIiIjRiVGJSomIiImRiUpRiZGJEYlRiUqJiIiKkYlKUYmRi1GJUYlKiZGKUYlKUYmIiInRiVGJSomIiIkRiUpRiYiIihGJUYlKiZGMEYlKUYmRilGJUYlKiZGMEYlKUYmRjBGJUYlKiZGJEYlKUYmIiM1RiVGJSokKUYmIiM2RiVGJQ== LCwqJiIiJCIiIilJInhHNiIiIiZGJUYlKiYiIiVGJSlGJ0YrRiUhIiIqJkYrRiUpRidGJEYlRi0qJkYrRiUpRiciIiNGJUYlRiVGJQ== LCwqJiIiJiIiIilJInhHNiJGJEYlRiUqJiIiI0YlKUYnIiIlRiUhIiIqJClGJyIiJEYlRi0qJkYkRiUpRidGKkYlRiVGJ0Yl LCwqJClJInhHNiIiIiUiIiJGKComRidGKClGJSIiJEYoRigqJiIiI0YoKUYlRi1GKEYoRiVGKEYtISIi NyQsLCokKUkieEc2IiIiJSIiIkYpKiZGKEYpKUYmIiIkRilGKSomIiIjRikpRiZGLkYpRilGJkYpRi4hIiIsKCokRi9GKUYpKiYiIiZGKUYmRilGKUYsRik= <-- exit PartialFactorSplit (now at top level) = [x^4+4*x^3+2*x^2+x-2, x^2+5*x+3]} NyQsLCokKUkieEc2IiIiJSIiIkYpKiZGKEYpKUYmIiIkRilGKSomIiIjRikpRiZGLkYpRilGJkYpRi4hIiIsKCokRi9GKUYpKiYiIiZGKUYmRilGKUYsRik= {--> enter PartialFactorSplit, args = x^4+2*x^3+x^2-5*x-2, x, 2, 11 Ii0hPTlzVCcqKg== Ny4iIiQiIikiIioiIiUiIzUiIiZGJ0YjIiInRiZGKEYj LDoiIiQiIiIqJiIiKUYkSSJ4RzYiRiRGJComIiIqRiQpRiciIiNGJEYkKiYiIiVGJClGJ0YjRiRGJComIiM1RiQpRidGLkYkRiQqJiIiJkYkKUYnRjRGJEYkKiZGMUYkKUYnIiInRiRGJComRiNGJClGJyIiKEYkRiQqJkY4RiQpRidGJkYkRiQqJkYuRiQpRidGKkYkRiQqJkY0RiQpRidGMUYkRiQqJkYjRiQpRiciIzZGJEYk LCgqJiIiJSIiIkkieEc2IkYlISIiKiYiIiNGJSlGJiIiJEYlRigqJkYsRiUpRiZGKkYlRig= ISIj IiIi NyQiIiIsLCokKUkieEc2IiIiJUYjRiMqJiIiI0YjKUYnIiIkRiNGIyokKUYnRitGI0YjKiYiIiZGI0YnRiMhIiJGK0Yy <-- exit PartialFactorSplit (now at top level) = [1, x^4+2*x^3+x^2-5*x-2]} NyQiIiIsLCokKUkieEc2IiIiJUYjRiMqJiIiI0YjKUYnIiIkRiNGIyokKUYnRitGI0YjKiYiIiZGI0YnRiMhIiJGK0Yy expand((x^2+3*x-2)*(x^4-5*x^3-2*x^2-3*x+3)) mod 11; LDAqJClJInhHNiIiIiciIiJGKComIiIjRigpRiUiIiZGKCEiIiomIiIkRigpRiUiIiVGKEYoKiQpRiVGL0YoRigqJkYqRigpRiVGKkYoRi0qJkYxRihGJUYoRihGLEYo PartialFactorSplit(x^4-5*x^3-2*x^2-3*x+3,x,2,11); PartialFactorSplit(x^4+2*x^3+x^2-5*x-2,x,2,11); {--> enter PartialFactorSplit, args = x^4-5*x^3-2*x^2-3*x+3, x, 2, 11 Ii1ddUkza1E= Ny4iIiEiIiUiIiciIiRGJUYkIiIqRiVGJ0YnRiYiIiI= LDgqJiIiJSIiIkkieEc2IkYlRiUqJiIiJ0YlKUYmIiIjRiVGJSomIiIkRiUpRiZGLUYlRiUqJkYpRiUpRiZGJEYlRiUqJkYkRiUpRiYiIiZGJUYlKiYiIipGJSlGJkYpRiVGJSomRilGJSlGJiIiKEYlRiUqJkY1RiUpRiYiIilGJUYlKiZGNUYlKUYmRjVGJUYlKiZGLUYlKUYmIiM1RiVGJSokKUYmIiM2RiVGJQ== LCoiIiIhIiJJInhHNiJGIyomIiIlRiMpRiUiIiRGI0YjKiYiIiNGIylGJUYsRiNGIw== IiIh LCwqJClJInhHNiIiIiUiIiJGKComIiImRigpRiUiIiRGKCEiIiomIiIjRigpRiVGL0YoRi0qJkYsRihGJUYoRi1GLEYo NyQsLCokKUkieEc2IiIiJSIiIkYpKiYiIiZGKSlGJiIiJEYpISIiKiYiIiNGKSlGJkYwRilGLiomRi1GKUYmRilGLkYtRilGKQ== <-- exit PartialFactorSplit (now at top level) = [x^4-5*x^3-2*x^2-3*x+3, 1]} NyQsLCokKUkieEc2IiIiJSIiIkYpKiYiIiZGKSlGJiIiJEYpISIiKiYiIiNGKSlGJkYwRilGLiomRi1GKUYmRilGLkYtRilGKQ== {--> enter PartialFactorSplit, args = x^4+2*x^3+x^2-5*x-2, x, 2, 11 Ii1sIyo9Mllw Ny4iIiEiIiMiIiIiIihGJUYmIiIkIiIlIiInIiIpRihGJA== LDgqJiIiIyIiIkkieEc2IkYlRiUqJClGJkYkRiVGJSomIiIoRiUpRiYiIiRGJUYlKiQpRiYiIiVGJUYlKiZGK0YlKUYmIiImRiVGJSomRi1GJSlGJiIiJ0YlRiUqJkYwRiUpRiZGK0YlRiUqJkY2RiUpRiYiIilGJUYlKiZGO0YlKUYmIiIqRiVGJSomRjBGJSlGJiIjNUYlRiUqJkYkRiUpRiYiIzZGJUYl LCoiIiMiIiJJInhHNiIhIiIqJiIiJUYkKUYlIiIkRiRGJComRilGJClGJUYjRiRGJw== ISIj IiIi NyQiIiIsLCokKUkieEc2IiIiJUYjRiMqJiIiI0YjKUYnIiIkRiNGIyokKUYnRitGI0YjKiYiIiZGI0YnRiMhIiJGK0Yy <-- exit PartialFactorSplit (now at top level) = [1, x^4+2*x^3+x^2-5*x-2]} NyQiIiIsLCokKUkieEc2IiIiJUYjRiMqJiIiI0YjKUYnIiIkRiNGIyokKUYnRitGI0YjKiYiIiZGI0YnRiMhIiJGK0Yy expand((x^2+4*x+5)*(x^2-2*x+4)) mod 11; LCwqJClJInhHNiIiIiUiIiJGKComIiIjRigpRiUiIiRGKEYoKiQpRiVGKkYoRigqJiIiJkYoRiVGKCEiIkYqRjE= PartialFactorSplit(x^4-5*x^3-2*x^2-3*x+3,x,2,11); {--> enter PartialFactorSplit, args = x^4-5*x^3-2*x^2-3*x+3, x, 2, 11 Ii1CKylILHQo Ny4iIioiIzUiIiIiIigiIiVGJiIiKUYlRiNGKEYmIiIj LDoiIioiIiIqJiIjNUYkSSJ4RzYiRiRGJCokKUYnIiIjRiRGJComIiIoRiQpRiciIiRGJEYkKiYiIiVGJClGJ0YxRiRGJComRi1GJClGJyIiJkYkRiQqJiIiKUYkKUYnIiInRiRGJCokKUYnRi1GJEYkKiZGI0YkKUYnRjdGJEYkKiZGN0YkKUYnRiNGJEYkKiZGLUYkKUYnRiZGJEYkKiZGK0YkKUYnIiM2RiRGJA== LCoiIiUhIiJJInhHNiJGJComIiIjIiIiKUYlIiIkRilGKSomRiNGKSlGJUYoRilGJA== ISIj IiIi NyQiIiIsLCokKUkieEc2IiIiJUYjRiMqJiIiJkYjKUYnIiIkRiMhIiIqJiIiI0YjKUYnRjBGI0YuKiZGLUYjRidGI0YuRi1GIw== <-- exit PartialFactorSplit (now at top level) = [1, x^4-5*x^3-2*x^2-3*x+3]} NyQiIiIsLCokKUkieEc2IiIiJUYjRiMqJiIiJkYjKUYnIiIkRiMhIiIqJiIiI0YjKUYnRjBGI0YuKiZGLUYjRidGI0YuRi1GIw== PartialFactorSplit(x^4-5*x^3-2*x^2-3*x+3,x,2,11); {--> enter PartialFactorSplit, args = x^4-5*x^3-2*x^2-3*x+3, x, 2, 11 Ii1ZSEg7MXQ= Ny4iIiIiIiUiIigiIioiIiRGJkYjRiRGJkYjIiInIiIj LDoiIiJGIyomIiIlRiNJInhHNiJGI0YjKiYiIihGIylGJiIiI0YjRiMqJiIiKkYjKUYmIiIkRiNGIyomRi9GIylGJkYlRiNGIyomRi1GIylGJiIiJkYjRiMqJClGJiIiJ0YjRiMqJkYlRiMpRiZGKUYjRiMqJkYtRiMpRiYiIilGI0YjKiQpRiZGLUYjRiMqJkY3RiMpRiYiIzVGI0YjKiZGK0YjKUYmIiM2RiNGIw== LCoiIiUiIiIqJkYjRiRJInhHNiJGJEYkKiYiIiZGJClGJiIiJEYkISIiKiZGK0YkKUYmIiIjRiRGJA== LCYqJiIiJCIiIilJInhHNiJGJEYlISIiRiVGJQ== LCgqJClJInhHNiIiIiMiIiJGKComIiImRihGJUYoRigiIiRGKA== NyQsKCokKUkieEc2IiIiIyIiIkYpKiYiIiZGKUYmRilGKSIiJEYpLChGJEYpRiZGKUYpRik= <-- exit PartialFactorSplit (now at top level) = [x^2+5*x+3, x^2+x+1]} NyQsKCokKUkieEc2IiIiIyIiIkYpKiYiIiZGKUYmRilGKSIiJEYpLChGJEYpRiZGKUYpRik= PartialFactorSplit(x^4-5*x^3-2*x^2-3*x+3,x,2,11); {--> enter PartialFactorSplit, args = x^4-5*x^3-2*x^2-3*x+3, x, 2, 11 Ii1kTzAybDU= Ny0iIiUiIzUiIikiIiFGJiIiJkYnIiIqIiIiRilGIw== LDQiIiUiIiIqJiIjNUYkSSJ4RzYiRiRGJComIiIpRiQpRiciIiNGJEYkKiYiIiZGJClGJ0YuRiRGJComRi5GJClGJyIiJ0YkRiQqJiIiKkYkKUYnIiIoRiRGJCokKUYnRipGJEYkKiQpRidGNEYkRiQqJkYjRiQpRidGJkYkRiQ= LCoiIiIhIiIqJiIiJkYjSSJ4RzYiRiNGIyomIiIlRiMpRiciIiNGI0YkKiZGKkYjKUYnIiIkRiNGIw== LCYqJiIiJCIiIilJInhHNiJGJEYlRiVGJCEiIg== LCgqJClJInhHNiIiIiMiIiJGKEYlRihGKEYo NyQsKCokKUkieEc2IiIiIyIiIkYpRiZGKUYpRiksKEYkRikqJiIiJkYpRiZGKUYpIiIkRik= <-- exit PartialFactorSplit (now at top level) = [x^2+x+1, x^2+5*x+3]} NyQsKCokKUkieEc2IiIiIyIiIkYpRiZGKUYpRiksKEYkRikqJiIiJkYpRiZGKUYpIiIkRik= expand((x^2+x+1)*(x^2+5*x+3)) mod 11; LCwqJClJInhHNiIiIiUiIiJGKComIiImRigpRiUiIiRGKCEiIiomIiIjRigpRiVGL0YoRi0qJkYsRihGJUYoRi1GLEYo
<Text-field style="Heading 1" layout="Heading 1">13. Az AKS-teszt</Text-field>
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">14. A szita m\303\263dszerek alapjai</Font></Text-field>
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn